Model Predictive Control for Trajectory Planning Considering Constraints on Vertical Load Variation

Abstract

To address the issue of centrifugal force affecting the vertical load during the stability and trajectory planning of autonomous vehicles during high-speed cornering and obstacle avoidance, a model predictive control of trajectory planning and tracking is proposed that considers the roll factor using only a two-degrees-of-freedom vehicle dynamics model. Firstly, a trajectory planning controller is designed. As a predictive model, a dual-track two-degrees-of-freedom vehicle dynamics model is established. This model describes the relationship between tire lateral forces and vertical loads using a quadratic nonlinear tire model. To reflect the actual dynamic state of the vehicle, the controller incorporates a nonlinear constraint that considers vertical load variations. The nonlinear optimization problem is transformed into a simplified quadratic programming problem by using the Jacobian matrix method to linearize the constraints. By fitting a fourth-degree polynomial curve to the discrete points calculated by the replanning algorithm, an optimal collision-free trajectory is obtained. Secondly, an MPC trajectory tracking controller is designed to control the vehicle in real time along the optimal trajectory from the planning, incorporating control quantity constraints, control increment constraints, and lateral angle constraints to maintain the vehicle’s motion state. We transform the trajectory tracking control problem into a quadratic programming problem, solving for the optimal control sequence for the autonomous vehicle to track the trajectory, achieving an optimized solution and rolling time domain control. Finally, the effectiveness of the vehicle’s obstacle avoidance planning and tracking under high-speed double-lane-change maneuver conditions is validated using the Simulink simulation platform. The results indicate that the designed planning and tracking controllers effectively improve the obstacle avoidance planning and tracking control for high-speed autonomous vehicles.